Equidistribution of Primitive Normal Elements in Finite Fields
Abstract
Let $q=p^k$ be a prime power, let $n\geq2$ be an integer and let $\mathbb{F}_{q^n}$ be a finite field. It is shown that the set of primitive normal elements is a Salem set. Furthermore, it is proved that this set is strongly equidistributed in the finite field. Similar results are proved for the set of quadratic residues and the set of primitive roots modulo a large prime $p\geq 3$.
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 February 2026
- Language
- EN
- Document type
- Preprint